Table 1 Absolute errors for \(N=8\), \(k=3\), \(M=5\), various values of α when it goes to \(\alpha =1\), and comparison of the absolute error with HPM [33] and MVIM [36] in Example 1

0

2.5654e − 07

7.7371e − 07

1.3304e − 06

2.4878e − 06

2.0852e − 08

0

0

0.1

3.0943e − 03

2.5784e − 03

1.8021e − 03

4.2893e − 04

1.0496e − 06

6.4221e − 04

1.0323e − 04

0.2

5.0069e − 05

1.4518e − 04

5.8107e − 04

1.5436e − 04

1.2781e − 06

9.8905e − 03

1.9372e − 03

0.3

6.0134e − 03

4.7295e − 03

2.9859e − 03

5.8153e − 04

2.6500e − 06

4.7274e − 02

1.3430e − 02

0.4

9.8473e − 03

7.7664e − 03

4.9873e − 03

1.1538e − 03

9.4140e − 06

1.3911e − 01

4.2501e − 02

0.5

9.3915e − 03

7.2676e − 03

4.6473e − 03

1.1361e − 03

2.0053e − 05

3.1320e − 01

9.4534e − 02

0.6

6.2457e − 03

4.6540e − 03

2.8907e − 03

7.0416e − 04

1.9822e − 05

5.9479e − 01

1.7111e − 01

0.7

2.8244e − 03

1.9277e − 03

1.1064e − 03

2.1850e − 04

4.4881e − 05

1.0034e + 00

2.7047e − 01

0.8

5.3751e − 04

1.9959e − 04

1.2624e − 04

2.4006e − 05

2.4770e − 05

1.5504e + 00

3.8837e − 01

0.9

3.1315e − 04

3.5580e − 04

2.9325e − 04

6.4162e − 05

2.3675e − 05

2.2365e + 00

5.1885e − 01

1

1.6365e − 07

3.8611e − 08

2.5677e − 08

6.8794e − 07

6.9133e − 07

3.0511e + 00

6.5484e − 01